Physics M.C.Q (1 Marks)

In nuclear fusion reactions, the heavy isotopes of Hydrogen take part like deuterium ${ }_1 H^2$ and tritium ${ }_1 H^3$ as they have extra neutron.

The concept of atomic mass was proposed by William Prout. Early atomic mass theory was proposed by the English chemist William Prout in a series of published papers in $1815$ and $1816$. Known as Prout's Law, Prout suggested that the known elements had atomic weights that were whole number multiples of the atomic mass of hydrogen.

Modern atomic weight scale is based on $C−12.$
The standard unit for expressing the mass of atom is amu $($atomic mass unit$).$
It is equal to $\frac{1}{12}$ of the mass of an atom of carbon$-12$ equal to $1.6605 \times 10^{-19} \mathrm{~g}$.
amu is also called as avogram.
Avogram is a unit of mass and weight equal to one gram divided by the Avogadro's number.

Fusion reaction takes place at $10^7$k
So, the correct choice is $ 3 \times 10^6 \mathrm{~K} $

$2A \rightarrow B$
Possible if $B$ is more stable than $A$
$⟹$ Energy of $B$ is less than two atoms of $A$
$\mathrm{E}_2 < 2 \mathrm{E}_1$​

The atomic weight is a characteristic property of an element and can never vary.
The valency of an element can vary. For example, when the ion is in $+2$ and $+3$ oxidation state, its valency is $2$ and $3$ respectively.

Packing fraction is the mass defect per nucleon i.e. elementary particle in the nucleus. The difference between atomic weight and mass number i.e. mass of elementary particle in the nucleus is known as mass defect. Hence,
$\text{p}=\frac{\Delta\text{m}}{\text{A}}$
$\text{p}=\frac{\text{M - A}}{\text{A}}$

One $\text{a.m.u.}$ is defined as mass of $\frac{1}{12}th$ the mass of one carbon$-12$ atom.

Radioactive isotopes have unstable nucleus which emits energy and particles when it converts to stable form. Cobalt$-60$ is an isotope used to treat Cancer like problems.

Chlorine is a chemical element with the symbol $Cl$ and atomic number $17$. The second$-$lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them.

The difference between the sum of the masses of the constituent particles and the mass of an atom is called mass defect.
The energy released due to mass defect was given by Einstein
$E = \triangle mc^2$

$(BE)_{Hc} = 28\ MeV, A$ of $He = 4$
$(BE)_{He} = \frac{28}{4}\ MeV$
$= 7\ MeV$

Fusion reaction is the combining of atom to form heavier nuclei. Fusion reaction requires high temperature. God fusion to occur on earth a, we need a temperature of at least $100$ million degree Celsius. It is also an uncontrollable reaction.

From conservation of mass
$24 + 4 = x + 1$
$x = 28 − 1 = 27$

Protons and neutrons are present inside the nucleus and they exert strong attractive nuclear force on each other. These forces are equal in magnitude, irrespective of the charge present on the nucleons.
$\therefore$ $ \mathrm{F}_{\mathrm{pp}} = \mathrm{F}_{\mathrm{pn}} = \mathrm{F}_{\mathrm{nn}} $
Here,$ \mathrm{F}_{\mathrm{pp}} = \mathrm{F}_{\mathrm{pn}} = \mathrm{F}_{\mathrm{nn}} $
denote the magnitudes of the nuclear force by a proton on a proton, by a proton on a neutron and by a neutron on a neutron, respectively.

Density of water is $= 1000\ kg/m^3$
Density of sun $= 1.4\times 1000$
$= 1.4 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$

The average nuclear radius $(R)$ and the mass number of the element $(A)$ has the following relation:
$\text{R}=\text{R}_{0}\text{A}^{\frac{1}{2}}$
$\frac{\text{R}}{\text{R}_{0}}=\text{A}^{\frac{1}{3}}$
In $\Big(\frac{\text{R}}{\text{R}_0}\Big)=\frac{1}{3}$ In $A$
Therefore, the graph of ln$\Big(\frac{\text{R}}{\text{R}_0}\Big)$ versus ln $A$ is a straight line passing through the origin with slope $\frac{1}{3}.$

The electron emitted in beta radiation may originates from neutron and it increases the atomic number $1.$

Nuclear fusion reactions are the nuclear reactions in which two or smaller $($lighter$)$ nuclei combine to form a bigger $($heavier$)$ nucleus giving off a huge amount of energy.

Two protons exert strong attractive nuclear force and repulsive electrostatic force on each other. Nuclear forces are short range forces existing in the range of a few fms. Therefore, at a separation of 10nm, the electromagnetic force is greater than the nuclear force, i.e. $ \mathrm{F}_{\mathrm{e}}>>\mathrm{F}_{\mathrm{n}} $

Atomic number $=$ number of protons $= 16$
Mass number $=$ Number of protons $+$ number of neutrons
So the mass number of sulfur $= 32$

Hydrogen bomb is based on nuclear fusion. A large amount of nuclear energy is released by fusion of two light elements $($elements with low atomic numbers$).$
In a hydrogen bomb, two isotopes of hydrogen, deuterium $(1$ proton, $1$ neutron$)$ and tritium $(1$ proton, $2$ neutron$)$ are fused to form a nucleus of helium and a neutron.
This fusion releases $17.6\ MeV$ of energy. Also, there is no limit on the amount of the fusion that can occur.

$\beta^-$ decay: $_\text{Z}^\text{A}\text{​X}→_{\text{Z}+1}^{\text{A}}\text{​Y} + _{−1}^0\text{​e}$
Thus, the atomic number is increased in $\beta^-$ decay.

The nucleus of Tritium (${ }_1 \mathrm{H }^3$) contains $1$ proton and $2$ neutrons.
A neutron decays as $\text{n}\rightarrow\ \text{p}+\overline{\text{e}}+\overline{\text{v}},$ the nucleus may have $2$ protons and one neutron i.e., tritium will transform into ${ }_2 \mathrm{He}^3$. It means triton energy is less that of ${ }_2 \mathrm{He}^3$ nucleaus. Tirton energy is less than that of ${ }_2 \mathrm{He}^3$ nucleus, which simple mean transformation is not allowed energetically.

In fusion reaction $0.65\%$ of mass is converted into energy.
So, $0.65\%$ of mass is lost during nuclear fusion.